Efficient subgroup exponentiation in quadratic and sixth degree extensions

This paper describes several speedups for computation in the order p + 1 subgroup of F*(p2) and the order p2 - p + 1 subgroup of F*(p6). These results are in a way complementary to LUC and XTR, where computations in these groups are sped up using trace maps. As a side result, we present an efficient method for XTR with p ≡ 3 mod 4